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Welcome …
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Welcome to the _Physics-based Deep Learning Book_ 👋
**TL;DR**:
This document targets a practical and comprehensive introduction of everything
related to deep learning in the context of physical simulations.
As much as possible, all topics come with hands-on code examples in the form of Jupyter notebooks to quickly get started.
Beyond standard _supervised_ learning from data, we'll look at _physical loss_ constraints,
more tightly coupled learning algorithms with _differentiable simulations_, as well as
reinforcement learning and uncertainty modeling.
We live in exciting times: these methods have a huge potential to fundamentally change what we can achieve
with simulations.
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Some visual examples of numerically simulated time sequences. In this book, we explain how to realize algorithms that use neural networks alongside numerical solvers.Coming up
As a sneak preview, the next chapters will show:
How to train networks to infer a fluid flow around shapes like airfoils, and estimate the uncertainty of the prediction. This gives a surrogate model that replaces a traditional numerical simulation.
How to use model equations as residuals to train networks that represent solutions, and how to improve upon these residual constraints by using differentiable simulations.
How to more tightly interact with a full simulator for inverse problems. E.g., we’ll demonstrate how to circumvent the convergence problems of standard reinforcement learning techniques by leveraging simulators in the training loop.
Throughout this text, we will introduce different approaches for introducing physical models into deep learning, i.e., physics-based deep learning (PBDL) approaches. These algorithmic variants will be introduced in order of increasing tightness of the integration, and the pros and cons of the different approaches will be discussed. It’s important to know in which scenarios each of the different techniques is particularly useful.
Comments and suggestions
This book, where “book” stands for a collection of digital texts and code examples, is maintained by the TUM Physics-based Simulation Group. Feel free to contact us if you have any comments, e.g., via old fashioned email. If you find mistakes, please also let us know! We’re aware that this document is far from perfect, and we’re eager to improve it. Thanks in advance 😀! Btw., we also maintain a link collection with recent research papers.
{admonition} Executable code, right here, right now :class: tip We focus on Jupyter notebooks, a key advantage of which is that all code examples can be executed _on the spot_, from your browser. You can modify things and immediately see what happens -- give it a try... <br><br> Plus, Jupyter notebooks are great because they're a form of [literate programming](https://en.wikipedia.org/wiki/Literate_programming).
Thanks!
This project would not have been possible without the help of many people who contributed. Thanks to everyone 🙏 Here’s an alphabetical list:
Additional thanks go to Georg Kohl for the nice divider images
(cf. {cite}kohl2020lsim), Li-Wei Chen for the airfoil data
image, and to Chloe Paillard for proofreading parts of the document.
% future: % - Georg Kohl
Citation
If you find this book useful, please cite it via:
@book{thuerey2021pbdl,
title={Physics-based Deep Learning},
author={Nils Thuerey and Philipp Holl and Maximilian Mueller and Patrick Schnell and Felix Trost and Kiwon Um},
url={https://physicsbaseddeeplearning.org},
year={2021},
publisher={WWW}
}